6 people can paint 3 walls in 49 minutes. How many minutes will it take for 9 people to paint 7 walls? Round to the nearest minute.
We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 3\text{ walls}\\ p &= 6\text{ people}\\ t &= 49\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{3}{49 \cdot 6} = \dfrac{1}{98}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 7 walls with 9 people. $t = \dfrac{w}{r \cdot p} = \dfrac{7}{\dfrac{1}{98} \cdot 9} = \dfrac{7}{\dfrac{9}{98}} = \dfrac{686}{9}\text{ minutes}$ $= 76 \dfrac{2}{9}\text{ minutes}$ Round to the nearest minute: $t = 76\text{ minutes}$